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Approximable dimension and acyclic resolutions

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Koyama A., Sher R. B.

Fundamenta Mathematicae

1997

tom 152

nr 1

43-53

We establish the following characterization of the approximable dimension of the metric space X with respect to the commutative ring R with identity: $a-dim_R$ X ≤ n if and only if there exist a metric space Z of dimension at most n and a proper $UV^{n-1}$-mapping f:Z → X such that $\check H^n(f^-1}(x);R) = 0 $ for all x ∈ X. As an application we obtain some fundamental results about the approximable dimension of metric spaces with respect to a commutative ring with identity, such as the subset theorem and the existence of a universal space. We also show that approximable dimension (with arbitrary coefficient group) is preserved under refinable mappings.

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1 Fundamenta Mathematicae

1 Koyama A.

1 Sher R. B.

1 1997

Wyniki wyszukiwania

Approximable dimension and acyclic resolutions